form a polynomial f(x) with real coefficients given the following degree 5; zeros: -9,-i,3+i

Question

Please help me to solve this I am in math 1050

Answer 1

The two missing zeroes must counterbalance the two complex zeroes. f(x) is the product of factors: f(x)=(x+9)(x+i)(x-i)(x-3-i)(x-3+i)⇒(x+9)(x^2+1)(x^2-6x+10)⇒(x+9)(x^4-6x^3+11x^2-6x+10)

⇒x^5-6x^4+11x^3-6x^2+10x+9x^4-54x^3+99x^2-54x+90⇒

f(x)=x^5+3x^4-43x^3+93x^2-44x+90